1.4 Heat Transfer, Specific Heat, and Calorimetry

Heat transfer is all about energy moving between objects due to temperature differences. It happens through conduction, convection, and radiation until everything reaches the same temperature. Understanding these processes is key to grasping thermodynamics.

Specific heat capacity tells us how much energy it takes to change an object's temperature. We use this to calculate energy transfers and temperature changes in various scenarios. It's a crucial concept for understanding how materials behave when heated or cooled.

Heat Transfer and Specific Heat

Heat transfer between objects

• Heat transfers thermal energy from higher to lower temperature objects until thermal equilibrium is reached where both objects have the same temperature
• Conduction transfers heat through direct contact in solids, liquids, and gases at a rate dependent on the material's thermal conductivity (metals vs insulators)
• Convection transfers heat through fluid movement due to density differences caused by temperature variations (hot air rising, cold air sinking)
• Radiation transfers heat through electromagnetic waves without requiring a medium and can occur in a vacuum with emission and absorption dependent on the object's temperature and surface properties (Sun's radiation, infrared cameras)
• The rate of heat transfer is influenced by thermal resistance, which measures a material's ability to resist heat flow

Calculations with specific heat capacity

• Specific heat capacity $c$ quantifies the heat required to raise the temperature of 1 gram of a substance by 1°C, measured in J/(g·°C) or J/(kg·K) and varies for different substances (water vs metal)
• Change in thermal energy $Q$ relates to mass $m$, specific heat capacity $c$, and change in temperature $\Delta T = T_f - T_i$ by $Q = mc\Delta T$
• Calculate temperature change by rearranging to $\Delta T = \frac{Q}{mc}$ (heating water on a stove)
• Calculate energy required for a given temperature change using $Q = mc\Delta T$ (energy to boil water)
• Heat capacity, the product of mass and specific heat capacity, represents the total amount of heat needed to change an object's temperature by 1°C

Thermal properties of materials

• Latent heat is the energy required for a substance to change phase without changing temperature
• Thermal expansion describes how materials change size or volume in response to temperature changes
• Thermal diffusivity measures how quickly heat spreads through a material, combining thermal conductivity, density, and specific heat capacity

Calorimetry and Energy Conservation

Energy conservation in calorimetry

• Calorimetry measures heat transfer during physical and chemical processes (mixing substances, phase changes)
• Energy conservation states energy cannot be created or destroyed, only transferred or converted, so total energy remains constant in a closed system with heat lost by one object equaling heat gained by another $Q_{lost} = -Q_{gained}$
• Solve calorimetry problems using these steps:
  1. Identify objects involved in heat transfer
  2. Determine heat flow direction from higher to lower temperature
  3. Apply energy conservation $Q_{lost} = -Q_{gained}$
  4. Use specific heat equation $Q = mc\Delta T$ for each object
  5. Solve for unknown variable (final temperature, mass, specific heat capacity)
• Common calorimetry scenarios include:
  • Mixing substances at different temperatures (hot and cold water)
  • Heating or cooling a substance with an external source or sink (ice in a drink)
  • Phase changes at constant temperature (melting ice, boiling water)